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2 results

  • On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras

  • Leandro Cagliero, Fernando Szechtman
  • Journal:
    Canadian Mathematical Bulletin / Volume 57 / Issue 4 / 01 December 2014
    Published online by Cambridge University Press:
    20 November 2018, pp. 735-748
    Print publication:
    01 December 2014
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  • We describe all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,\,y\,\in \,K$. When is $F\left[ x,\,y \right]\,=\,F\left[ \alpha x\,+\,\beta y \right]$ for some nonzero elements $\alpha ,\,\beta \,\in \,F?$

  • On the Decomposition of Nonsingular CS-Modules

  • John Clark, Nguyen Viet Dung
  • Journal:
    Canadian Mathematical Bulletin / Volume 39 / Issue 3 / 01 September 1996
    Published online by Cambridge University Press:
    20 November 2018, pp. 257-265
    Print publication:
    01 September 1996
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  • It is shown that if M is a nonsingular CS-module with an indecomposable decomposition M = ⊕i∊I Mi, then the family {Mi | i € I} is locally semi-T"- nilpotent. This fact is used to prove that any nonsingular self-generator Σ-CS module is a direct sum of uniserial Noetherian quasi-injective submodules. As an application, we provide a new proof of Goodearl's characterization of non-singular rings over which all nonsingular right modules are projective.